Third harmonic (TH) generation is a commonly used nonlinear optical process that triples the input photon energy. Large conversion efficiency in traditional nonlinear optical devices requires large nonlinearities, low material absorption, and phase-matching techniques that increase the interaction length to the millimeter-to-centimeter range. Phase matching is irrelevant at the nanoscale, and new strategies must be developed to boost the performance of sub-wavelength nonlinear optical devices which are expected to play an important role in optoelectronics and optical information processing. Several approaches involving high-Q photonic modes have been proposed, including ring cavity modes, guided mode resonances, photonic crystal band edges, and defect states of periodic structures. See M. Kauranen and A. V. Zayats, Nature Photonics 6, 737 (2012). Recently, metallic and more generally plasmonic nanostructures have received considerable attention. See J. A. Schuller et al., Nat Mater 9, 193 (2010); and A. V. Zayats et al., Physics Reports 408 (2005). While the Q-factors of plasmonic resonators are usually smaller than those achieved with all-dielectric photonic devices, larger field enhancements are possible since plasmonic modal volumes can be deeply sub-wavelength. However, harmonic generation using the sub-wavelength structures reported thus far relies on field enhancements associated with localized surface plasmon resonances or collective resonances that require exquisite fabrication techniques. See M. Kauranen and A. V. Zayats, Nature Photonics 6, 737 (2012); L. Scaccabarozzi et al., Opt. Lett. 31, 3626 (2006); B. Corcoran et al., Nat Photon 3, 206 (2009); J. Lee et al., Nature 511, 65 (2014); and S. Campione et al., Applied Physics Letters 104, 131104 (2014).
Therefore, a need remains for a means for harmonic light generation in a sub-wavelength nonlinear optical device.